Large-scale Coherent Vortices Research Articles

Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets

The invariants of the velocity gradient (R and Q), rate-of-strain (RS and QS), and rate-of-rotation (QW) tensors are analyzed across the turbulent/nonturbulent (T/NT) interface by using a direct numerical simulation (DNS) of a turbulent plane jet at Reλ≈120. The invariants allow a detailed characterization of the dynamics, geometry and topology of the flow during the entrainment. The invariants Q and QS are almost equal and negative outside the turbulent region close to the T/NT interface, which shows the existence of high values of strain product (hence viscous dissipation of kinetic energy) at that location. Right at the T/NT interface, the invariants QW and QS show that virtually all flow points there are characterized by irrotational dissipation, with no discernible sign of the coherent structures which are known to exist deep inside the turbulent region. Moreover, the invariants of the velocity gradient tensor (Q and R) show that the classical “teardrop” shape of their associated phase map is not yet formed at the T/NT interface. All the invariants rapidly change after the T/NT interface is crossed into the turbulent region. For instance, the enstrophy density, proportional to QW, is zero in the irrotational flow region and high and more or less constant inside the turbulent region, after it undergoes a sharp jump near the T/NT interface. Inside the turbulent region, at a distance of only 1.7η from the T/NT interface, where η is the Kolmogorov microscale, the invariants QW and QS suggest that large scale coherent vortices already exist in the flow. Furthermore, the joint probability density function of Q and R already displays its well known teardrop shape at that location. Moreover, the geometry of the straining (or deformation) of the fluid elements during the turbulent entrainment process is preferentially characterized by biaxial expansion with αS:βS:γS=2:1:−3, where αS, βS, and γS are the eigenvalues of the rate-of-strain tensor arranged in descending order. Based on an analysis of the invariants, many aspects of the flow topology inside the turbulent region at a distance of only 1.7η from the T/NT interface are already similar to those observed deep inside the turbulent region.

Characteristics of strongly-forced turbulent jets and non-premixed jet flames

Previous researchers have demonstrated that strong pulsations of the fuel flow rate can significantly reduce the flame length and luminosity of laminar/transitional non-premixed jet flames. The physical mechanisms responsible for these changes are investigated experimentally in acoustically-forced jet flows where the peak velocity fluctuations are up to eight times the mean flow velocity. Both reacting and non-reacting flows were studied and Reynolds numbers, based on the mean flow properties, ranged from 800 to 10,000 (corresponding to peak Reynolds numbers of 1,450–23,000), and forcing frequencies ranged from 290 to 1,140 Hz. Both the first and second organ-pipe resonance modes of the fuel delivery tube were excited to obtain these frequencies. An analysis of the acoustic forcing characteristics within the resonance tube is provided in order to understand the source of the high amplitude forcing. Flow visualization of jets with first resonant forcing confirms the presence of large-scale coherent vortices and strong reverse flow near the exit of the fuel tube. With second-resonant forcing, however, vortices are not emitted from the tube as they are drawn back into the fuel tube before they can fully form. Increased fine-scale turbulence is associated with both resonant cases, but particularly at second resonance. The power spectra of the velocity fluctuations for a resonantly pulsed jet show the presence of an inertial subrange indicating that the flow becomes fully turbulent even for mean-Reynolds-number jets that are nominally laminar. It is shown that these pulsed jet flows exhibit strong similarities to synthetic jets and that the Strouhal number, based on the maximum velocity at the fuel tube exit, is the dominant parameter for scaling these flows. The Strouhal number determines the downstream location where the coherent vortices breakdown, and is found to provide better collapse of flame length data (both current and previous) than other parameters that have been used in the literature.

Formation of Secondary Vortices in Turbulent Square-Duct Flow

A linear approach, inspired by hydrodynamic stability theory, is used to describe the formation of large-scale coherent vortices for the turbulent flow that develops in a duct of square cross section. A set of equations for small-amplitude coherent motion is derived and closed with a simple mixing-length strategy. The initial condition that maximizes a chosen functional (related to either the kinetic energy of the coherent motion or the rate of turbulence production) is found through a direct/adjoint numerical approach borrowed from optimal control theory. It is found that different kinds of secondary flows can appear in the duct cross section, sustained by the mean shear. Some of these optimal states display a symmetry about the bisectors and the diagonals of the duct, in agreement with experimental observations and direct numerical simulations.

Transport and Collective Dynamics in Suspensions of Confined Swimming Particles

Direct simulations of large populations of confined hydrodynamically interacting swimming particles at low Reynolds number are performed. Hydrodynamic coupling between the swimmers leads to large-scale coherent vortex motions in the flow and regimes of anomalous diffusion that are consistent with experimental observations. At low concentrations, swimmers propelled from behind (like spermatazoa) strongly migrate toward solid surfaces in agreement with simple theoretical considerations; at higher concentrations this localization is disrupted by the large-scale coherent motions.

Turbulence Production and Energy Transfer Mechanism in the Transition Process of a Two-Dimensional Jet

The effects of coherent vortices on turbulent energy transfer were examined in an acoustically excited two-dimensional parabolic jet. Production terms in the energy transport equation were evaluated based on the results of hotwire conditional measurements. Difference in vortex arrangement gave significant influence on the energy transport process among mean flow, coherent structure and incoherent turbulence. When the symmetrical vortex arrangement was excited, most of the mean flow energy directly dissipated into random incoherent turbulence. For the anti-symmetrical mode, large amounts of positive and negative turbulent energy fluxes were produced around strong large-scale coherent vortices. Fine-scale vortices between the streamwisely adjacent coherent vortices played important roles in the turbulent energy transport process for the anti-symmetrical vortex arrangement.

A new electromagnetic wave and associated vortex motions in nonuniform dusty magnetoplasmas

It is known that the presence of stationary charged dust grains produces rotational ion motion due to the J × B force in a uniform dusty magnetoplasma, where J is the plasma current density and B is the magnetic field. Our objective here is to show the possibility of a new low-frequency electromagnetic mode in a nonuniform dusty magnetoplasma. The nonlinear dynamics of newly found electromagnetic mode is governed by a Charney–Hasegawa–Mima (C-HM) equation. Possible stationary solutions of the latter can be represented in the form of a vortex street and a dipolar vortex. The present results should help to understand the origin of large scale coherent vortex structures that are frequently observed in astrophysical objects (e.g., in molecular clouds) and in galaxies. Besides, new laboratory experiments should be conducted for verifying the linear and nonlinear properties of the low-frequency electromagnetic wave that is reported herein.

Coherent structures and their stability in ion temperature gradient turbulence

Periodic arrays of large scale coherent vortices and their stability have been investigated, within the framework of /spl eta//sub i/ turbulence, using two-dimensional fluid simulation in slab geometry. These vortices, in combination with viscosity damping of small scales, contribute to the formation of a steady state in a system with linearly unstable modes. The steady state comprises of a few vortex convective turn over times and seems to be fairly robust. It has been recognized that a vortex chain, consisting of positive and negative vorticities, continues to move stably in the poloidal direction (along periodic direction). On the other hand, an initial isolated monopole vortex is unstable and leads to a long-lived stable dipolar structure after a few vortex turnover periods. A variety of simple collisional interaction processes among these coherent vortices have also been explored numerically.

Coherent Structures in Flat-Bed Abutment Flow: Computational Fluid Dynamics Simulations and Experiments

Numerical computations and laboratory experiments are carried out to investigate the three-dimensional structure of large-scale (coherent) vortices induced by bridge abutments on a flat bed. A finite-volume numerical method is developed for solving the unsteady, three-dimensional Reynolds-averaged Navier–Stokes equations, closed with the k-ω turbulence model, in generalized curvilinear coordinates and applied to study the flow in the vicinity of a typical abutment geometry with a fixed, flat bed. The computed flowfields reveal the presence of multiple, large-scale, unsteady vortices both in the upstream, “quiescent,” region of recirculating fluid and the shear-layer emanating from the edge of the foundation. These computational findings motivated the development of a novel experimental technique for visualizing the footprints of large-scale coherent structures at the free surface. The technique relies on digital photography and employs averaging of instantaneous images over finite-size windows to extract ...

Practical Aspects in Comparing Shock-Capturing Schemes for Dam Break Problems

Numerical computations and laboratory experiments are carried out to investigate the three-dimensional structure of large-scale (coherent) vortices induced by bridge abutments on a flat bed. A finite-volume numerical method is developed for solving the unsteady, three-dimensional Reynolds-averaged Navier–Stokes equations, closed with the k–ω turbulence model, in generalized curvilinear coordinates and applied to study the flow in the vicinity of a typical abutment geometry with a fixed, flat bed. The computed flowfields reveal the presence of multiple, large-scale, unsteady vortices both in the upstream, “quiescent,” region of recirculating fluid and the shear-layer emanating from the edge of the foundation. These computational findings motivated the development of a novel experimental technique for visualizing the footprints of large-scale coherent structures at the free surface. The technique relies on digital photography and employs averaging of instantaneous images over finite-size windows to extract coherent eddies from the chaotic turbulent flow. Application of this technique to several abutment configurations yielded results that support the numerical findings.

Combustion dynamics of turbulent swirling flames

In the present paper the influence of a periodic excitation of the mass flow rate, varied in frequency and in amplitude, on the isothermal flow field and on the flame characteristics of swirl burners with different swirl intensities S 0,th is investigated. At first the fluid dynamical conditions for the formation of ring-vortex structures in the burner near flow field are determined. The results indicate that the minimum level of excitation of the mass flow rate for vortex formation decreases hyperbolically with increasing frequency of pulsation and characteristic Strouhal number, respectively. In further studies, the dynamical behavior of lean-premixed swirl flames is investigated, whereas the fuel gas/air mixture mass flow rate at the burner exit was modulated sinusoidally. The dynamical behavior of the investigated flames is found to be dominated by two different effects in certain frequency ranges: For moderate pulsation frequencies (f puls ≲ 50 Hz) the detected periodic heat release rate of pulsated, premixed swirl flames is dominated by an effect that inhibits the strong entrainment of ambient medium in comparison with the corresponding quasi steady-state swirl flames. With increasing frequency (f puls ≳ 50 Hz) this effect will be overlaid by the periodical formation of ring-vortices entraining additional ambient medium and interfering with the combustion process. The physical understanding of the frequency-dependent flame dynamics (flame transfer function) on periodic disturbances is indispensable for the prediction of the formation of combustion-driven oscillations that occur in technical combustion systems (e.g., gas turbines, industrial combustors). It is also evident for the development of methods to prevent or suppress periodic combustion instabilities. The results of the flame transfer measurements presented in this paper will lead to a basic understanding of the formation and reaction of large-scale coherent vortex structures in turbulent flames, that are well known as drivers of combustion instabilities.

VISUALIZATION AND TIME-FREQUENCY ANALYSIS ON COHERENT VORTICES GENERATED BEHIND DUNE

Large-scale coherent vortices such as separated vortex and kolk-boil are often observed and generated behind crest of sand dunes in actual flood rivers. The kolk-boil vortex greatly affects transport of suspended sediment that develops up to free-surface. In the present study, visualization by dye-injection technique and turbulence measurement by a laser Doppler anemometer were simultaneously conducted in order that the whole and instantaneous structure of vortices could be clarified. Then, wavelet analysis was applied by means of time series of turbulence fluctuation. Then, distinctive properties could be seen in convection velocity, wavelength and frequency of generation and so on.

Derivation of Maximum Entropy Principles in Two-Dimensional Turbulence via Large Deviations

The continuum limit of lattice models arising in two-dimensional turbulence is analyzed by means of the theory of large deviations. In particular, the Miller–Robert continuum model of equilibrium states in an ideal fluid and a modification of that model due to Turkington are examined in a unified framework, and the maximum entropy principles that govern these models are rigorously derived by a new method. In this method, a doubly indexed, measure-valued random process is introduced to represent the coarse-grained vorticity field. The natural large deviation principle for this process is established and is then used to derive the equilibrium conditions satisfied by the most probable macrostates in the continuum models. The physical implications of these results are discussed, and some modeling issues of importance to the theory of long-lived, large-scale coherent vortices in turbulent flows are clarified.

Effects of Chemical Reaction on Two-Dimensional Turbulence

Direct numerical simulations of compressible two-dimensional homogeneous turbulent reacting flows are conducted to investigate the interactions between turbulence and chemical reaction. Both isothermal and exothermic nonpremixed reactions are considered. In isothermal reacting simulations, the turbulence is not affected by the reaction and is characterized by the large scale coherent vortices and vorticity-gradient sheet structures. The spatial structures of the density and temperature fields are similar to that of vorticity. However, mixing and reaction occur in the layer like (lamellar) structures which are mainly formed in the hyperbolic flow regions, where the vorticily-gradient sheets are present and the turbulent stretching dominates the circulation. Analysis of the simulations with exothermic reactions indicates that the heat of reaction has significant influence on thc spatial and the compositional structure of velocity, scalar and thermodynamic variables. The fluctuations of the density, the temperature, the pressure and the dilatation are substantially increased due to nonuniform heat release. The heat of reaction also modifies the small scale solenoidal velocity field. At early times, when the reaction is significant, the magnitude of the vorticity (enstrophy) is enhanced by the baroclinic vorticity generation. At late times, when the reaction is almost completed, the molecular dissipation is dominant and the magnitude of vorticity decays continuously. Examination of the energy transfer among the rotational and the compressive components of the kinetic energy and the internal energy indicates that the energy of reaction is transfered to the compressive component of the kinetic energy by the pressure-dilatation correlations. The turbulent advection then transfer the energy from the compressive component of the kinetic energy to its rotational component.

Three-dimensional structure of space-time correlation on coherent vortices generated behind dune crest

Large-scale coherent vortices such as separated vortices and kolk-boils are often observed and generated behind crests of sand dunes in fluvial rivers. The kolk-boil vortex greatly affects transport of suspended sediment which develops up to the free surface. In the present study, both visualization by dye-injection technique and turbulence measurements with a laser Doppler anemometer were conducted in order that the elemental structure of vortices could be clarified. 3-D space-time structures of the coherent vortices are discussed by evaluating conventional correlation coefficients and also by using conditional sampling techniques. Instantaneous velocity-velocity combinations at different points were simultaneously measured by means of two sets of laser Doppler anemometers and an automatic traversing system. Refined physical models of coherent vortices are proposed in the present study.

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ ≃ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.

On the influence of a large scale coherent vortex on the turbulent cascade

Abstract. We investigate the flow between coaxial rotating disks in the situation where a strong axial vortex is present over a turbulent background. This is nonstationary and inhomogeneous as is common in most turbulent geophysical flows. We describe the s scale statistics using tools recently introduced for homogeneous turbulent flows. It seems that the cascade cess is preserved although modified by the large coherent structure.

Energy Budget around Large-Scale Coherent Vortex in Turbulent Boundary Layer.

The terms of the coherent energy equation were experimentally evaluated for a large-scale coherent vortex developed in a turbulent boundary Layer. X and Y components of the terms were chiefly concentrated around the symmetrical plane between the two legs of the coherent Vortex where the outflow occurred, whereas Z components were distributed along the central axes of the legs at about Z/δ=±0.3. The mean advection, the coherent production, the random production and the random diffusion were dominant in the energy equation. The dissipation was about two orders of magnitude smaller than the production, which suggested that most of the coherent energy was dissipated by the random production and the random diffusion.

Measurements of the stabilization zone of a lifted jet flame under acoustic excitation

The turbulence and concentration characteristics in the stabilization zone of a lifted jet flame with and without acoustic excitation are measured by a time-resolved Rayleigh scattering, a LDV, and a hot vire anemometry system together with other probes. Both amplification and suppression of the flow can be achieved by acoustic excitation. By careful comparison of the turbulence and concentration characteristics in the stabilization zone for the natural, amplification and suppression cases, it is found that the key parameters of lifted flame stabilization in the stabilization zone are the integral length scale, the F probability of the presence of a flammable premixture, and the G probability of the presence of a fluid with a temperature reaching the ignition temperature. Amplification excitation enhances the large-scale coherent vortices and the vortical entrainment, thus enhancing the length scale, theF probability, and the G probability of having a combustibltoe premixture in the stabilization zone. In this case, the flame shifts upstream to a higher gas speed location and restabilizes there. Suppression excitation shows the opposite results. Practical need calls for a new model capable of predicting the stabilization zone structure of excited lifted flames where the large length scale, theF andG probabilities are suggested to be important parameters.

Wavelet analysis of 2D turbulent fields

Two descriptions of turbulent two-dimensional incompressible flows are at hand: the à la Kolmogorov spectral scenario is based on non-linear interactions between scales and cascade processes, when the coherent structures description deals with spatially localized interacting structures. The spectral approach leads to universal spectral or dispersion laws which often fail to be verified as this approach does not take into account the strong spatial variability of the flow. Conversely the coherent structure description does not provide quantitative predictions. From the Lagrangian point of view the two types of description have led to different approaches for the study of turbulent transport; namely, global self-similar theories and local parameterizations of turbulent dispersion. To reconcile these two kind of approaches tentatives have been made to separate flow fields into regions having different dynamical behaviours. However to achieve this program we need tools to obtain quantitative information on the dynamical properties of these different regions. To this end, orthonormal multidimensional wavelet decompositions are presented on a theoretical and practical basis as a preliminary step towards the goal of properly parameterizing Eulerian and Lagrangian properties of turbulent flows. Wavelet coefficients are interpreted from the viewpoint of turbulence analysis and used to extract form the flow field spatially localized spectral informations, giving a simultaneous description of the flow field in physical space (vortices and structures, intermittency) and in spectral space (energy or enstrophy spectra and cascades). Applications of the wavelet analysis are given for two-dimensional flows exhibiting a strong spatial variability; one is related to an unforced temporal mixing layer, the other to forced homogeneous incompressible turbulence. In both cases, the wavelet analysis points out clearly that small scales are dominant in shear zones, outside large scale vortices and that local spectral slopes are much different within a large scale coherent vortex, a shear zone, or the intersticial flow.

Turbulence Production by a Large-Scale Horseshoe Vortex in a Turbulent Boundary Layer.

The triple decomposition analysis derives three components of the production term from the turbulence energy equation : the mean production of coherent motion, the mean production of incoherent turbulence, and the coherent production of incoherent turbulence. The present experiment evaluated these terms around a large-scale coherent vortex in a fully developed turbulent boundary layer. These quantities were accumulated between the legs of the horseshoe vortex where the ejection occurred. The coherent motion was mainly produced through the stretching of the leg vortices caused by the mean velocity shear. The negative distribution of the mean production of incoherent turbulence shows that incoherent turbulence partly recovers the momentum of the mean flow deformed by the coherent motion of the vortex.